This invention relates to an apparatus and method for measuring and monitoring complex permittivity of materials.
Microstrip and microstrip type resonators described are efficient devices for measuring complex permittivity of materials at microwave frequencies as disclosed by Flemming U.S. Pat. No. 4,829,233; by Heath U.S. Pat. No. 3,510,764; and by Gerhard U.S. Pat. No. 3,942,107 and by King U.S. Pat. No. 5,334,941. Flemming describes a method in which a resonator is mounted or the copper-backed substrate. A resonator is weakly coupled to a microwave feed source and to a microwave detector so that the resonator Q factor is unaffected by the impendances of the source or the detector. When the test dielectric is placed near the resonator, the electromagnetic fields near the resonator are coupled to the material under test so as to affect the resonator frequency of resonance, as well as Q factor.
The resonator frequency and Q factor measurements are done in the transmission mode. Further the methods for modulating source or resonant frequency are disclosed which avoids the need for the swept source.
Heath uses a half wavelength microstrip resonator, which is tightly sandwiched between two sheets of sample test material. These sheets of sample material are clamped in a special fixture. The microstrip resonator is loosely capacitively coupled to the microstrip feed line, which passes near one end of the resonator normal to the resonator length. The dielectric constant is determined from the measurement of resonant frequency and Q factor for the transmission between sensor""s two input and output ports. As the special cutting and positioning of thin sheets of the sample material is required; Heath""s method is not in situ or non-destructive.
King relates to the use of a microwave reflection resonator sensor for complex permittivity measurement in situ. The microstrip resonator is fed from the ground plane side through a slot.
Microwave power is coupled to the slot through a coaxial line or a microstrip. The material under test is kept in contact with the sensor. The resonant frequency and input power coupling factor is measured at the resonant frequency. The real and imaginary parts of permittivity (∈xe2x80x2 and ∈xe2x80x3) or the conductivity ("sgr") are determined from the resonant frequency and coupling coefficient data using approximate closed form expressions. King uses bottom fed resonators which King claims to be a major modification but this leads to complicated assembly and unstable mounting compared to the side-coupled resonator. The approximation in the basic expression of capacitance of the cross section of the sensor leads to the serious inaccuracies in the results. The closed form expressions need to use standards for calibration to evaluate constants. King depends upon empirical or analytical calibration. Evaluation of the constants before the installation and commissioning of the sensor is essential. The starting equation of effective capacitance of King is based on the assumption that the fringing field constant is the same for all thicknesses of a sample. Our analysis (FIG. 12) shows that the resonant frequency varies with the permittivity, as well as material thickness. King is limited to the measurement of infinitely thick samples only. The empirical calibration techniques of King leads to errors if the thickness of the sample is different than the calibration standard. While King is directed to an in situ sensor, it is not possible to perform in situ calibrations in most situations, as the chamber cannot be filled with the calibration liquid or solid. Therefore, King leads to errors in the calculated and true data due to calibrations using standards. The same is true for the analytical calibrations as the actual surface irregularities and air gaps between the resonator and the solid sample contribute to the errors in measurements. It is essential to validate analytical technique with the standard data. Dispersion in microstrip with dielectric overlay also plays an important part in errors. None of the empirical calibration techniques using closed form expressions account for dispersion. The shifts in the resonant frequency can be larger than 1 GHz at the material permittivities of 10 (FIG. 13). Hence, dispersion affects accuracy at the first decimal place of permittivity. Both Flemming and Heath involve transmission from one input port to an output port. Both ports are loosely and capacitively coupled to the intervening resonator by capacitive coupling. King relates only to the critically coupled reflection one port sensor. King relates to samples of very large size compared to the sensor. Gerhard relates to the measurement real part of the dielectric constant only. The samples under consideration are thin sheets of dielectric materials.
Gabelich measures dielectric homogeneity at 100 KHz to 2 MHz for the use of dielectric substrates for CTS-ESA radar antennas on Barium STrontium Titanate (BST). The C band or microwave permittivity is co-related to low frequency permittivity even though it is not accurate enough. Further, Gabelich measures only the real part of permittivity.
U.S. Pat. No. 5,686,841 Nov. 11, 1997, Stolarczyk et. al teach the use of patch antenna to detect presence of ice, water and/or antifreeze mixtures on wings of the aircraft or roads. A single frequency is fed to the antenna which is one of the arms of the bridge circuit. This frequency is varied until admittance of the antenna approaches zero. The object of the Stolarczyk""s invention is not to accurately determine complex or real permittivity but to only detect formation of ice. The frequency resolution of the frequency variation is very low, of the order of 2.4 MHz.
A primary object of this invention is to propose a process and apparatus for the measurement and monitoring of complex permittivity and conductivity of materials in situ which is accurate.
Another object of this invention is to propose a process and apparatus for the measurement and monitoring of complex permittivity and conductivity of materials in situ using automatic scalar or vector network analyzers or swept frequency generators and peak detectors that perform fast and accurate frequency and amplitude measurements.
Still another object of this invention is to propose a process and apparatus for the measurement and monitoring of complex permittivity and conductivity of materials in situ employing online numerical analysis software performing numerous iterations to arrive at convergence within few seconds with required accuracy like xc2x10.1 or xc2x10.01 in case of ∈ and xc2x10.0001 or xc2x10.0005 in case of ∈.
Yet another object of this invention is to propose a process and apparatus for the measurement and monitoring of complex permittivity and conductivity of materials in situ and wherein the determination of real and imaginary parts of permittivity takes place in a relatively short period.
A further object of this invention is to propose a process and apparatus for the measurement and monitoring of complex permittivity and conductivity of materials in situ and wherein the permittivity measurement does not depend on the first order approximations and simplistic closed form expressions involving unknown constants.
A still further object of this invention is to propose a process and apparatus for the measurement and monitoring of complex permittivity and conductivity of materials in situ where the materials used may be one of high frequency circuits boards, various bulk polymers and semiconductor materials.
Yet a further object of this invention is to propose a process and apparatus for the measurement and monitoring of complex permittivity and conductivity of materials in situ and wherein transmission type resonators may be used for samples of smaller size than the resonator.
The invention provides a device and process for measuring and monitoring complex permittivity of materials for quality control, in situ and in the materials measurement laboratory. Material under test is kept as an overlay on a microstrip, asymmetric stripline, co-planar waveguide, patch or a disc resonator. The resonator has its resonant frequency in the range of 0.5 to 20 GHz. The material is placed in contact with the top conductors of the circuits or with a finite air gap above the top conductor. The ground plane at the top may or may not be used. A fringing field from the top surface and the edges of the resonator passes through the material under test, which is kept as an overlay dielectric. As the fields above the substrate pass through the material under test the effective permittivity of the resonator increases. The Q factor (Q=xcex2/2xcex1) of the resonator changes due to a change in the propagation constant (xcex2) and attentuation constant (xcex1). An increase in the effective permittivity of a microstrip, asymmetric stripline, coplanar waveguide resonator, rejection filter, patch or a disc causes a decrease in the resonant frequency of the resonator. That is, the Q factor of the resonator decreases as the attenuation due to overlay adds to the total losses.
The invention envisages the use of transmission as well as reflection type resonators. The resonators are coupled to the source of microwave power using direct or gap coupling (capacitively or inductively) from the side of the microstrip conductor and not from the ground plane side. The measurements may be one port or two port depending upon the dimensions of the material under test. If a swept frequency source is used then a resonant dip may be observed in the reflection or transmission mode with the available instrument accuracy. The Q factor is directly measured using half power frequencies and the resonant frequency. The unloaded Q measurement is preferred for the accurate measurement ∈xe2x80x3 or "sgr". If a loaded Q is measured, then it is necessary to calculate an unloaded Q from the loaded Q factor. The resonant or half power frequencies may be automatically or manually measured and fed to the computer using a data acquisition system and/or frequency tracking device. The dedicated computer program calculates real and imaginary parts of the complex permittivity or conductivity of the material under test. The program is based on the numerical analysis of a microstrip embedded in multiple dielectric layers, the material under test being the layer of unknown permittivity.